Unstructured Finite Volume Method Research Articles

Application of Unstructured Finite Volume Method in Structural Static Mechanics

Unstructured finite volume method applied in structural static mechanics has been discussed to direct at the difficulty of dealing with irregular boundary, unstructured triangle elements have been used in computational domain, the basic equations of unstructured finite volume method applied in structural static mechanics has been deduced. Comparing the unstructured grids with the structured grids, the former has obvious advantage on dealing with irregular boundary by theoretical analysis. According to examples analysis, the comparison of numeric results with analytic solutions and FEM solutions showed the effectiveness of the unstructured finite volume method.

A numerical analysis of solid–liquid phase change heat transfer around a horizontal cylinder

A numerical study is conducted to analyze the melting process around a horizontal circular cylinder in the presence of the natural convection in the melt phase. Two boundary conditions are investigated one of constant wall temperature over the surface of the cylinder and the other of constant heat flux. A numerical code is developed using an unstructured finite-volume method and an enthalpy porosity technique to solve for natural convection coupled to solid–liquid phase change. The validity of the numerical code used is ascertained by comparing our results with previously published results.

2D Unstructured Mesh Finite Volume Method for Simulating Structural Dynamics

A novel procedure for calculating the dynamic response of elastic solid structures is presented. The ultimate aim of this study is to develop a consistent set of finite volume (FV) methods on unstructured meshes for the analysis of dynamic fluidstructure interaction (FSI). This paper describes a two-dimensional (2D) FV cell-vertex based method for dynamic solid mechanics. A novel matrix-free implicit scheme was developed using the Newmark method and dual time step algorithm and the model is validated with a 2D cantilever test case as well as a 2D plate one.

A Study of Physical and Numerical Effects of Dissipation on Turbulent Flow Simulations

ABSTRACT: The present work is primarily concerned with studying the effects of artificial dissipation and of certain diffusive terms in the turbulence model formulation on the capability of representing turbulent boundary layer flows. The flows of interest in the present case are assumed to be adequately represented by the compressible Reynolds-averaged Navier-Stokes equations, and the Spalart-Allmaras eddy viscosity model is used for turbulence closure. The equations are discretized in the context of a general purpose, density-based, unstructured grid finite volume method. Spatial discretization is based on the Steger-Warming flux vector splitting scheme and temporal discretization uses a backward Euler point-implicit integration. The work discusses in detail the theoretical and numerical formulations of the selected model. The computational studies consider the turbulent flow over a flat plate at 0.3 freestream Mach number. The paper demonstrates that the excessive artificial dissipation automatically generated by the original spatial discretization scheme can deteriorate boundary layer predictions. Moreover, the results also show that the inclusion of Spalart-Allmaras model cross-diffusion terms is primarily important in the viscous sublayer region of the boundary layer. Finally, the paper also demonstrates how the spatial discretization scheme can be selectively modified to correctly control the artificial dissipation such that the flow simulation tool remains robust for high-speed applications at the same time that it can accurately compute turbulent boundary layers.

A time-domain finite volume approach for prediction of muffler transmission loss including thermal effects

A time-domain finite volume approach is presented for predicting the transmission loss of muffler including thermal effects with non-uniform sound speed field and density field, in which the acoustic wave equation in heterogeneous media is solved by using unstructured finite volume method with the temperature field specified or solved by some commercial code. An improved time-domain impulse method based on the absorbing boundary condition is applied to predict the acoustic attenuation characteristics of mufflers. The approach is validated by numerical simulations of a simple expansion chamber muffler and a complex muffler with five chambers. The predicted results agree well with the corresponding experimental ones and numerical ones obtained by finite element method with commercial code SYSNOISE. The results of both mufflers under different thermal conditions indicate that the temperature distribution has a significant influence on transmission loss. According to the analysis of a complex muffler with ideal medium, it is shown that the variation of working conditions can obviously affect density and sound speed distributions but have little influence on transmission loss. On the other hand, the obtained transmission loss with the solved temperature field deviates much from the one with specified uniform temperature field.

An Unstructured Finite-Volume Method for Transient Heat Conduction Analysis of Multilayer Functionally Graded Materials with Mixed Grids

An unstructured finite-volume time-domain method (UFVTDM) is developed to solve two-dimensional transient heat conduction in multilayer functionally graded materials (FGMs). A four-node quadrilateral grid and a three-node triangular grid are employed to deal with mixed-grid problems. The accuracy of the method is improved by treating the quadrilateral grid as a bilinear element with consideration of both the linear term and the constant term. The improvement is validated to be vital to avoid violent numerical oscillation when applying the method to heat point-source problems. The accuracy and capability of the UFVTDM are validated by numerical tests.

Application of a line implicit method to fully coupled system of equations for turbulent flow problems

For unstructured finite volume methods, we present a line implicit Runge–Kutta method applied as smoother in an agglomerated multigrid algorithm to significantly improve the reliability and convergence rate to approximate steady-state solutions of the Reynolds-averaged Navier–Stokes equations. To describe turbulence, we consider a one-equation Spalart–Allmaras turbulence model. The line implicit Runge–Kutta method extends a basic explicit Runge–Kutta method by a preconditioner given by an approximate derivative of the residual function. The approximate derivative is only constructed along predetermined lines which resolve anisotropies in the given grid. Therefore, the method is a canonical generalisation of point implicit methods. Numerical examples demonstrate the improvements of the line implicit Runge–Kutta when compared with explicit Runge–Kutta methods accelerated with local time stepping.

303 非圧縮性流れに対する非構造移動格子有限体積法

When we simulate flows on moving-grid time-dependently, the Moving-Grid Finite-Volume Method is crucial. The method was firstly proposed for compressible flows. Subsequently, the method for incompressible flows was applied to the structured grid, but it has not been applied to the unstructured grid yet. The unstructured grid is crucial to simulate flows with the complex-shaped body. On the other hand, the influence of flows driven by body-motion is important. In this paper, we propose a new Unstructured Moving-Grid Finite-Volume Method based on fractional step method for incompressible flows. Moreover, we apply this method to the coupled problem of fluid-flow and body-motion.

Parallel large-scale numerical simulations of purely-elastic instabilities behind a confined circular cylinder in a rectangular channel

The parallel large-scale unstructured finite volume method proposed in [Sahin, A stable unstructured finite volume method for parallel large-scale viscoelastic fluid flow calculations, J. Non-Newtonian Fluid Mech. 166 (2011) 779–791] has been applied to investigate the three-dimensional creeping flow of an Oldroyd-B fluid past a confined circular cylinder in a rectangular channel at relatively high Weissenberg numbers. The numerical method is based on side-centered finite volume method where the velocity vector components are defined at the mid-point of each cell face, while the pressure term and the extra stress tensor are defined at element centroids. The present arrangement of the primitive variables leads to a stable numerical scheme and it does not require any ad-hoc modifications in order to enhance the pressure–velocity–stress coupling. The combination of the present numerical method with the log-conformation representation proposed in [R. Fattal, R. Kupferman, Constitutive laws for the matrix-logarithm of the conformation tensor, J. Non-Newtonian Fluid Mech. 123 (2004) 281–285] and the geometric non-nested multilevel preconditioner for the Stokes system have enabled us to simulate large-scale viscoelastic fluid flow problems on highly parallel machines. The calculations are presented for an Oldroyd-B fluid past a confined circular cylinder in a rectangular channel at relatively high Weissenberg numbers and compared to those obtained for Newtonian fluids. The present numerical calculations reveal three-dimensional purely-elastic instabilities in the wake of a confined single cylinder which is in accord with the earlier experimental results in the literature. In addition, the flow field is found out to be no longer symmetric in the wake of the cylinder at high Weissenberg numbers.

An unstructured finite volume method for impact dynamics of a thin plate

The examination of an unstructured finite volume method for structural dynamics is assessed for simulations of systematic impact dynamics. A robust display dual-time stepping method is utilized to obtain time accurate solutions. The study of impact dynamics is a complex problem that should consider strength models and state equations to describe the mechanical behavior of materials. The current method has several features. 1) Discrete equations of unstructured finite volume method naturally follow the conservation law. 2) Display dual-time stepping method is suitable for the analysis of impact dynamic problems of time accurate solutions. 3) The method did not produce grid distortion when large deformation appeared. The method is validated by the problem of impact dynamics of an elastic plate with initial conditions and material properties. The results validate the finite element numerical data.

Coupled analysis of unsteady aerodynamics and vehicle motion of a road vehicle in windy conditions

The two-way coupling of full-scale vehicle motion and the surrounding turbulence motion has been realized on a developed unsteady aerodynamic simulator for a road vehicle. A large-eddy simulation (LES) technique has been applied to reproduce the unsteady turbulence motion, and an unstructured finite volume method has been adopted to explain the complicated geometry of a full-scale road vehicle. Three-degree-of-freedom equations of the vehicle’s dynamic motion are incorporated into the developed LES code, and the motion is numerically reproduced by coupling the arbitrary Lagrangian–Eulerian (ALE) method and Navier–Stokes equations in a non-inertial reference frame. The simulation code is implemented on a massively parallel processor to meet the demands of the large-scale, long-term aerodynamic simulations of full-scale road vehicles. As a typical application of the coupled analysis, an unsteady aerodynamics simulation of a simplified heavy-duty truck in windy conditions is demonstrated, and the effects of the unsteady aerodynamics on the truck’s motion are investigated. The obtained results are compared with the results of a conventional quasi-steady analysis, and certain differences in the vehicle path and the yaw angle are identified. The effects of the transitional aerodynamics on variables related to driver’s perception are significant. These results clearly indicate the importance of estimating the unsteady aerodynamic forces in a vehicle motion analysis.

Two-Dimensional Numerical Model for Scalar Transport by Finite Volume Method on Unstructured Grid

Based on arbitrarily unstructured shallow water current model and finite volume method, a high-order non-oscillatory transport model is constructed. The stability and non-oscillatory condition of the transport model are also analyzed in theory. Usually, the maximum allowable time steps of current model and transport model are different, so an unsynchronized technique is used for the flow and the transport model computations to improve computational efficiency. In addition, the conservation of transport model during the unsynchronized computation is ensured by the time integration of currents continuity equation. Apply this model to the salinity transport simulation of Oujiang estuary, numerical results show that the water level, velocity and salinity agree well with the measured data.

The use of an axisymmetric formulation of the Finite Volume Method for the thermal analysis of the retina and ocular tissues following implantation of retinal prosthesis

This study analyzes the heat transfer in human eyes following implantation of retinal prostheses using an axisymmetric formulation of the Finite Volume Method. The model used consisted of a vertex centered unstructured grid finite volume method in an edge-based data structure and an explicit time integration. The results of the finite volume thermal analysis in ocular tissues were determined in the presence of two types of retinal implants: subretinal and epiretinal. For the subretinal device, the maximum temperature reached in the retina was 36.78°C (309.78 K) and the irreversible thermal damage occurred at 200 days. In the case of the epiretinal implant, the maximum temperature reached at the retinal/chip interface was 36.92°C (309.92 K) and the irreversible thermal damage occurred at 180 days. Our results indicate that tin spite of its higher dissipation power, the epiretinal implant produces thermal damages similar to that caused by the subretinal implant. The computational tool which was developed was able to effectively calculate temperature profiles and thermal damage values to retinal implants and is also capable to calculate temperature profile in any other geometry of interest, for example with other types s of external thermal source like laser beans.

Enhancement of Heat Transfer Using Delta-Winglet Type Vortex Generators with a Common-Flow-up Arrangement

Simulations of a coolant air flowing in a heat exchanger with delta-winglet type vortex generators in common-flow-up configuration have been performed to unveil the salient heat transfer characteristics. The heat exchanger is approximated as a periodic rectangular channel with heated walls and a pair of built-in tubes near the inlet and outlet. The heat transfer characteristics of the heat exchangers with vortex generators near the inlet, outlet, and both inlet and outlet have been compared. The Navier-Stokes equations together with the energy equation are solved employing unstructured finite volume method. The simulations reveal a significant enhancement in heat transfer because of the strong swirling motion originating from the streamwise longitudinal vortices behind the pair of delta winglets. The spiraling flow entrains air into the core and causes intermixing of the fluid layers to disrupt the growth of the thermal boundary layer. A parametric study on the angles of attack identifies the conditions under which enhancement in heat transfer can lead to significant miniaturization of the heat exchangers. The analysis also reveals interesting flow structures behind the winglets and correlates them to the mechanism of heat transfer.

Generalized flooded agglomerate model for the cathode catalyst layer of a polymer electrolyte membrane fuel cell

The flooded agglomerate model has found prolific usage in modeling the oxygen reduction reaction within the cathode catalyst layer of a polymer electrolyte membrane fuel cell (PEMFC). The assumption made in this model is that the ionomer-coated carbon–platinum agglomerate is spherical in shape and that the spheres are non-overlapping. This assumption is convenient because the governing equations lend themselves to closed-form analytical solution when a spherical shape is assumed. In reality, micrographs of the catalyst layer show that the agglomerates are best represented by sets of overlapping spheres of unequal radii. In this article, the flooded agglomerate is generalized by considering overlapping spheres of unequal radii. As a first cut, only two overlapping spheres are considered. The governing reaction-diffusion equations are solved numerically using the unstructured finite-volume method. The volumetric current density is extracted for various parametric variations, and tabulated. This sub-grid-scale generalized flooded agglomerate model is first validated and finally coupled to a computational fluid dynamics (CFD) code for predicting the performance of the PEMFC. Results show that when the agglomerates are small (<200nm equivalent radius), the effect of agglomerate shape on the overall PEMFC performance is insignificant. For large agglomerates, on the other hand, the effect of agglomerate shape was found to be critical, especially for high current densities for which the mass transport resistance within the agglomerate is strongly dependent on the shape of the agglomerate, and was found to correlate well with the surface-to-volume ratio of the agglomerate.

Mathematical modeling of catalytic wet oxidation in trickle-bed reactors by a diffusion–convection–reaction approach embedded with an interstitial CFD framework

In this work, we propose a diffusion–convection–reaction methodology to gain further insights into the heterogeneous multiphase flow of trickle beds. Our case-study encompasses a multi-fluid model embedded within an interstitial framework on the numerical simulation of continuous catalytic wet oxidation of hazardous compounds. First, with the proviso that phase holdup, pressure drop, and liquid distribution are fundamental criteria for the efficient design of trickle beds, the multiphase flow constitutive equations have been developed and solved by the conservative unstructured finite volume method. Second, several numerical variables were parametrically optimized based on the application of different under-relaxation parameters, mesh densities, and time stepping strategies. The segregated solver has been found to reveal good properties in terms of convergence and stability criteria, which endorsed the further corroboration. Finally, this theoretical probing-sensing scheme enabled the characterization of liquid flow texture accomplished by three-dimensional flow patterns exposing their deviation from ideal plug flow. The diffusion–convection–reaction framework coupled within a CFD model can then be further exploited on the simulation of complex multiphase reactive flows with adjustable parameters.

An Unstructured Finite-Volume Method for Structure–Electrostatics Interactions in MEMS

Radio-frequency microelectromechanical systems (RF MEMS) are widely used for contact actuators and capacitive switches, and involve metal–dielectric contact. In these devices, the structure is activated by an electrostatic force, whose magnitude changes as the gap closes. It is advantageous to model fluid and structural mechanics and electrostatics within a single comprehensive numerical framework to facilitate coupling between them. In this article, we extend a cell-based finite-volume approach popularly used to simulate fluid flow to characterize structure–electrostatics interactions. The method employs fully implicit second-order finite-volume discretization of the integral conservation equations governing elastic solid mechanics and electrostatics, and uses arbitrary convex polyhedral meshes. Results are presented in this article for a fixed-fixed beam under electrostatic actuation.

Unstructured finite volume method for matrix free explicit solution of stress–strain fields in two dimensional problems with curved boundaries in equilibrium condition

In this paper, a plane stress structural solver which uses a matrix free unstructured finite volume method based on Galerkin approach is introduced for solution of weak form of two dimensional Cauchy equations on linear triangular element meshes. The developed shape function free Galerkin finite volume structural solver explicitly computes stresses and displacements in cartesian coordinate directions for the two dimensional solid mechanic problems in equilibrium condition. The accuracy of the introduced algorithm is assessed by comparison of computed results of two plane-stress cases with curved boundaries under uniformly distributed loads with available analytical solutions. The results of the introduced method are presented in terms of stress and strain contours and its effective parameters on convergence behaviour to equilibrium condition are assessed.

An unstructured finite volume time domain method for structural dynamics

An unstructured finite volume time domain method (UFVTDM) is proposed to simulate stress wave propagation, in which the original variables of displacement and stress are solved based on the dynamic equilibrium equations. An Euler explicit and unstructured finite volume method is used for time dependent and spacial terms respectively. The displacements are stored on the cell vertex and a vertex based finite volume method is formed with that integral surface and the stresses are as assumed to be uniform in the cell. The present UFVTDM has several features. (1) The governing equations are discretized with the finite volume method which naturally follows conservation laws. (2) It can handle complex engineering problem. (3) This method is also able to analyze the natural characteristics and the numerical experiment shows that it is very efficient. Several cases are used to show the capability of the algorithm.

Impact of shape of container on natural convection and melting inside enclosures used for passive cooling of electronic devices

The present paper numerically analyzes a passive cooling system using enclosures with different geometries filled with thermal conductivity-enhanced phase change material (PCM). A numerical code is developed using an unstructured finite-volume method and an enthalpy-porosity technique to solve for natural convection coupled to a solid-liquid phase change. Five geometries containing the same volume of PCM are compared while cooling the same surface. The unsteady evolution of the melting front and the velocity and temperature fields is detailed. Other indicators of cooling efficiency are monitored, including the maximum temperature reached at the cooled surface. The computational results show the high impact of varying geometry: a maximum temperature difference as high as 40^{\circ}C is observed between two of the enclosures. The best efficiency is obtained for an enclosure shifted vertically relative to the cooled surface. Other findings and recommendations are made for the design of PCM-filled enclosures.